Solve =2x^4+9x^3-9x-3

$$= 2 x ^ { 4 } + 9 x ^ { 3 } - 9 x - 3$$

Differentiate w.r.t. x

$$8x^{3}+27x^{2}-9$$

Steps Using Derivative Rule for Sum

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$4\times 2x^{4-1}+3\times 9x^{3-1}-9x^{1-1}$$

Multiply 4 times 2.

$$8x^{4-1}+3\times 9x^{3-1}-9x^{1-1}$$

Subtract 1 from 4.

$$8x^{3}+3\times 9x^{3-1}-9x^{1-1}$$

Multiply 3 times 9.

$$8x^{3}+27x^{3-1}-9x^{1-1}$$

Subtract 1 from 3.

$$8x^{3}+27x^{2}-9x^{1-1}$$

Subtract 1 from 1.

$$8x^{3}+27x^{2}-9x^{0}$$

For any term t except 0, t^{0}=1.

$$8x^{3}+27x^{2}-9$$

Evaluate

$$2x^{4}+9x^{3}-9x-3$$